### Video Transcript

A data set has summary statistics
π π₯π₯ is equal to 36.875, π π¦π¦ is 73.875, and π π₯π¦ is 32.375. Calculate the product-moment
correlation coefficient for this data set, giving your answer correct to three
decimal places.

We are given the summary statistics
for a data set, where π π₯π₯ is 36.875; thatβs the variation in π₯. π π¦π¦ is 73.875; thatβs the
variation in π¦. And π π₯π¦ is 32.375; thatβs the
covariance of π₯ and π¦. And using these summary statistics,
we want to calculate the product-moment correlation coefficient. To do this, we can use the
abbreviated form of the correlation coefficient formula. That is, the correlation
coefficient π π₯π¦ is π π₯π¦ divided by the square root of π π₯π₯ times π
π¦π¦.

Since weβre given the summary
statistics, we simply need to substitute these into the formula. So that π π₯π¦ is 32.375, thatβs
π π₯π¦, divided by the square root of the product of 36.875, which is π π₯π₯, and
73.875, which is π π¦π¦. That is 32.375 over the square root
of 2724.140625, which is 32.375 divided by 52.19330 to five decimal places. And thatβs approximately
0.62029. And so to three decimal places, the
product-moment correlation coefficient for this data set is π π₯π¦ is equal to
0.620.